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Chapter 1: Problem 27

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Short Answer

Expert verified
The dimensions of the tennis court are 36 feet in width and 78 feet in length.

Step by step solution

01

Define the Variables

Let鈥檚 define the width of the rectangle as \(x\) feet, and because the length is 6 feet longer than twice the width, define the length as \(2x + 6\) feet.
02

Write Out the Perimeter Formula

In this case, a rectangular perimeter equals twice the sum of the length and the width: \(P = 2*(l + w)\). Substituting the specified parameter \(P = 228\) feet: \(228 = 2*(2x + 6 + x)\).
03

Solve the equation

Solve for \(x\) using algebra: Simplify the equation to \(228 = 2*(3x + 6)\), which will give \(114 = 3x + 6\). Further simplifying, subtract 6 from both sides to get \(108 = 3x\), then divide both sides by 3 which will yield \(x = 36\). This value corresponds to the width. Substitute \(x = 36\) into \(2x + 6\) to find the length, which equals \(78\) feet.

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